Thyroid cancer is a malignant neoplasm originated from thyroid cells. It can be classified into papillary carcinomas (PTCs) and anaplastic carcinomas (ATCs). Although ATCs are in an very aggressive status and cause more death than PTCs, their difference is poorly understood at molecular level. In this study, we focus on the transcriptome difference among PTCs, ATCs and normal tissue from a published dataset including 45 normal tissues, 49 PTCs and 11 ATCs, by applying a machine learning method, maximum relevance minimum redundancy, and identified 9 genes (BCL2, MRPS31, ID4, RASAL2, DLG2, MY01B, ZBTB5, PRKCQ and PPP6C) and 1 miscRNA (miscellaneous RNA, LOC646736) as important candidates involved in the progression of thyroid cancer. We further identified the protein-protein interaction (PPI) sub network from the shortest paths among the 9 genes in a PPI network constructed based on STRING database. Our results may provide insights to the molecular mechanism of the progression of thyroid cancer.